No, it only means that for players that are new to the pro leagues. I think its something like 3 years or less, then they do not need waivers. However, because Guenin has been playing for over 3 years, he's eligible for waivers no matter what.

Like, Elliott and Barrie WILL be eligible for waivers next year, even if we sign them to 2 way contracts

No. Two-way has no impact on waivers, but means that if a player is sent down to the AHL, there is already a negotiated rate that he will make there. If he's on a one-way contract, the player will make his NHL rate regardless of whether he plays in the AHL (or even CHL/ECHL) or NHL.